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A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm, with its end closer to the pole at a distance of 20 cm from the mirror. Find the length of the image of the rod.

1. 2.5 cm
2. 5 cm
3. 10 cm
4. 15 cm

Correct answer: 10 cm

Solution

For a concave mirror with f = -10 cm (using sign convention, distances measured from pole, mirror on left): End A at u = -20 cm: 1/v_A + 1/(-20) = 1/(-10) => 1/v_A = -1/10 + 1/20 = -1/20 => v_A = -20 cm. End B at u = -30 cm: 1/v_B + 1/(-30) = 1/(-10) => 1/v_B = -1/10 + 1/30 = -2/30 = -1/15 => v_B = -15 cm. Length of image = |v_A - v_B| = |-20 - (-15)| = 5 cm. Answer: 5 cm.

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